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Densities for piecewise deterministic Markov processes with boundaryJun 13 2019We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In our approach ... More

Perturbation theory and higher order $\mathcal{S}^p$-differentiability of operator functionsJun 13 2019We establish, for $1 < p < \infty$, higher order $\mathcal{S}^p$-differentiability results of the function $\varphi : t\in \mathbb{R} \mapsto f(A+tK) - f(A)$ for selfadjoint operators $A$ and $K$ on a separable Hilbert space $\mathcal{H}$ with $K$ element ... More

A Noninequality for the Fractional GradientJun 13 2019In this paper we give a streamlined proof of an inequality recently obtained by the author: For every $\alpha \in (0,1)$ there exists a constant $C=C(\alpha,d)>0$ such that \begin{align*} \|u\|_{L^{d/(d-\alpha),1}(\mathbb{R}^d;\mathbb{R}^d)} \leq C \| ... More

N-dimensional Heisenberg's uncertainty principle for fractional Fourier transformJun 13 2019A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional fractional Fourier ... More

Spectral semi-Fredholm theory on Hilbert C*-modulesJun 12 2019Given an A-linear, bounded, adjointable operator F on the standard module H_A; we consider the operators of the form F - a1 as a varies over Z(A) and this gives rise to a different kind of spectra of F in Z(A) as a generalization of ordinary spectra of ... More

Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomersJun 12 2019We compute the relaxation of the total energy related to a variational model for nematic elastomers, involving a nonlinear elastic mechanical energy depending on the orientation of the molecules of the nematic elastomer, and a nematic Oseen--Frank energy ... More

m-isometric operators and their local propertiesJun 12 2019In this paper we give necessary and sufficient conditions for a bounded linear Hilbert space operator to be an $m$-isometry for an unspecified $m$ written in terms of conditions that are applied to "one vector at a time". We provide criteria for orthogonality ... More

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysisJun 12 2019We use techniques from time-frequency analysis to show that the space $\mathcal S_\omega$ of rapidly decreasing $\omega$-ultradifferentiable functions is nuclear for every weight function $\omega(t)=o(t)$ as $t$ tends to infinity. Moreover, we prove that, ... More

Amenability and harmonic $L^p$-functions on hypergroupsJun 12 2019Let $K$ be a locally compact hypergroup with a left invariant Haar measure. We show that the Liouville property and amenability are equivalent for $K$ when it is second countable. Suppose that $\sigma$ is a non-degenerate probability measure on $K$, we ... More

Torus computed tomographyJun 12 2019We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization ... More

On the volume of unit balls of finite-dimensional Lorentz spacesJun 12 2019We study the volume of unit balls $B^n_{p,q}$ of finite-dimensional Lorentz sequence spaces $\ell_{p,q}^n.$ We give an iterative formula for ${\rm vol}(B^n_{p,q})$ for the weak Lebesgue spaces with $q=\infty$ and explicit formulas for $q=1$ and $q=\infty.$ ... More

Modified log-Sobolev inequality for a compact PJMP with degenerate jumpsJun 11 2019We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced ... More

LocLets: Localized Graph Wavelets for Processing Frequency Sparse Signals on GraphsJun 11 2019In this article, a new family of graph wavelets, abbreviated LocLets for \textit{Loc}alized graph wave\textit{Lets}, is introduced. These wavelets are localized in the Fourier domain on subsets of the graph Laplacian spectrum. LocLets are built upon the ... More

Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensionsJun 11 2019We prove that a general class of nonlinear, non-autonomous ODEs in Fr\'echet spaces are close to ODEs in a specific normal form, where closeness means that solutions of the normal form ODE satisfy the original ODE up to a residual that vanishes up to ... More

A nonlinear Lazarev-Lieb theorem: $L^2$-orthogonality via motion planningJun 11 2019Lazarev and Lieb showed that finitely many integrable functions from the unit interval to $\mathbb{C}$ can be simultaneously annihilated in the $L^2$ inner product by a smooth function to the unit circle. Here we answer a question of Lazarev and Lieb ... More

First-order linear evolution equations with càdlàg-in-time solutionsJun 10 2019In this work we study first-order linear parabolic evolution PDEs over $\mathbb{R}^{d}\times\mathbb{R}$ and $\mathbb{R}^{d}\times\mathbb{R}^{+}$ comprising a spatial operator defined through a symbol function and a source term such that its spatial Fourier ... More

An Optimal Plank TheoremJun 10 2019It is shown that for any sequence $v_1,v_2,\dots,v_n$ of unit vectors in a real Hilbert space $H$, there exists a unit vector $v$ in $H$ such that $$|\langle v_k,v \rangle| \geq \sin(\pi/2n)$$ for all $k$. This a sharp version of the plank theorem for ... More

Dot product invariant valuations on Lip$(S^{n-1})$Jun 10 2019We provide an integral representation for continuous, rotation invariant and dot product invariant valuations defined on the space Lip$(S^{n-1})$ of Lipschitz continuous functions on the unit $n-$sphere.

A Lyapunov Approach to Robust Regulation of Distributed Port-Hamiltonian SystemsJun 10 2019This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port-Hamiltonian systems including second order models such as the Euler-Bernoulli beam. The control design is achieved using the internal ... More

On the Riesz Transforms for the inverse Gauss measureJun 10 2019Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian function. Let further $\mathscr{A}$ be the natural self-adjoint Laplacian on $L^2(\gamma_{-1})$. In this paper, we prove that the Riesz ... More

Norms of weighted sums of log-concave random vectorsJun 09 2019Let $C$ and $K$ be centrally symmetric convex bodies of volume $1$ in ${\mathbb R}^n$. We provide upper bounds for the multi-integral expression \begin{equation*}\|{\bf t}\|_{C^s,K}=\int_{C}\cdots\int_{C}\Big\|\sum_{j=1}^st_jx_j\Big\|_K\,dx_1\cdots dx_s\end{equation*} ... More

A note on norms of signed sums of vectorsJun 09 2019Our starting point is an improved version of a result of D. Hajela related to a question of Koml\'{o}s: we show that if $f(n)$ is a function such that $\lim\limits_{n\to\infty }f(n)=\infty $ and $f(n)=o(n)$, there exists $n_0=n_0(f)$ such that for every ... More

Decomposition of the tensor product of two Hilbert modulesJun 09 2019Given a pair of positive real numbers $\alpha, \beta$ and a sesqui-analytic function $K$ on a bounded domain $\Omega \subset \mathbb C^m$, in this paper, we investigate the properties of the sesqui-analytic function $\mathbb K^{(\alpha, \beta)}:= K^{\alpha+\beta}\big(\partial_i\bar{\partial}_j\log ... More

Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spacesJun 09 2019The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for a complete ... More

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood--Paley Characterizations and Real InterpolationJun 09 2019Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, assuming that the powered Hardy--Littlewood maximal operator satisfies some Fefferman--Stein vector-valued maximal inequality on $X$ as well as it is bounded on both the ... More

Banach limits -- Some new thoughts and perspectivesJun 09 2019The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional analysis as ... More

The spectrum of composition operators induced by a rotation in the space of all analytic functions on the discJun 09 2019A characterization of those points in the unit disc which belong to the spectrum of a composition operator $C_{\varphi}$, defined by a rotation $\varphi(z)=rz$ with $|r|=1$, on the space $H_0(\mathbb{D})$ of all analytic functions on the unit disc which ... More

High-dimensional limit theorems for random vectors in $\ell_p^n$-balls. IIJun 09 2019In this article we prove three fundamental types of limit theorems for the $q$-norm of random vectors chosen at random in an $\ell_p^n$-ball in high dimensions. We obtain a central limit theorem, a moderate deviations as well as a large deviations principle ... More

Linear Dimension Reduction Approximately Preserving a Function of the 1-NormJun 08 2019For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are not too close, ... More

Roe- Strichartz Theorem on Two Step Nilpotent Lie GroupsJun 08 2019Strichartz characterized eigenfunctions of the Laplacian on Euclidean spaces by boundedness conditions which generalized a result of Roe for the one-dimensional case. He also proved an analogous statement for the sublaplacian on the Heisenberg groups. ... More

Lifschitz tail for alloy-type models driven by the fractional LaplacianJun 08 2019We establish precise asymptotics near zero of the integrated density of states for the random Schr\"{o}dinger operators $(-\Delta)^{\alpha/2} + V^{\omega}$ in $L^2(\mathbb R^d)$ for the full range of $\alpha\in(0,2]$ and a fairly large class of random ... More

Twin semigroups and delay equationsJun 08 2019In the standard theory of delay equations, the fundamental solution does not `live' in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, ... More

The regulator problem for the one-dimensional Schrodinger equation via the backstepping approachJun 08 2019We investigate the regulator problem (tracking and disturbance rejection) for a system (plant) described by a boundary controlled anti-stable linear one-dimensional Schrodinger equation, using the backstepping approach. The output to be controlled is ... More

Semi-Fredholm Theory on Hilbert C*-modulesJun 07 2019In this paper we establish the semi-Fredholm theory on Hilbert C*-modules as a continuation of Fredholm theory on Hilbert C*-modules established by Mishchenko and Fomenko. We give a definition of a semi-Fredholm operator on Hilbert C*-module and prove ... More

Hypercontractivity, and Lower Deviation Estimates in Normed SpacesJun 07 2019We consider the problem of estimating probabilities of lower deviation $\mathbb P\{\|G\| \leqslant \delta \mathbb E\|G\|\}$ in normed spaces with respect to the Gaussian measure. These estimates occupy central role in the probabilistic study of high-dimensional ... More

Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processingJun 07 2019In this paper we study the problem of the convergence in variation for the generalized sampling series based upon averaged-type kernels in the multidimensional setting. As a crucial tool, we introduce a family of operators of sampling-Kantorovich type ... More

Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spacesJun 07 2019In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in X$, where ... More

Planar sampling sets for the short-time Fourier transformJun 07 2019This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling bound in the ... More

Hardy-space function theory, operator model theory, and dissipative linear systems: the multivariable, free-noncommutative, weighted Bergman-space settingJun 06 2019Jun 10 2019It is known that (i) a subspace ${\mathcal N}$ of the Hardy space $H^2$ which is invariant under the backward shift operator can be represented as the range of the observability operator of a conservative discrete-time linear system, (ii) the transfer-function ... More

Hardy-space function theory, operator model theory, and dissipative linear systems: the multivariable, free-noncommutative, weighted Bergman-space settingJun 06 2019It is known that (i) a subspace ${\mathcal N}$ of the Hardy space $H^2$ which is invariant under the backward shift operator can be represented as the range of the observability operator of a conservative discrete-time linear system, (ii) the transfer-function ... More

The Navier--Stokes equations in exterior Lipschitz domains: $\mathrm{L}^p$-theoryJun 06 2019We show that the Stokes operator defined on $\mathrm{L}^p_{\sigma} (\Omega)$ for an exterior Lipschitz domain $\Omega \subset \mathbb{R}^n$ $(n \geq 3)$ admits maximal regularity provided that $p$ satisfies $| 1/p - 1/2| < 1/(2n) + \varepsilon$ for some ... More

Linear perturbations of the Wigner transform and the Weyl quantizationJun 06 2019We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner transform, but in ... More

A note on eigenvalues estimates for one-dimensional diffusion operatorsJun 06 2019Dealing with one-dimensional diffusion operators, we obtain upper and lower variational formulae on the eigenvalues given by the max-min principle, generalizing the celebrated result of Chen and Wang on the spectral gap. Our inequalities reveal to be ... More

Ideal boundedness of subseries and rearrangements in Banach spaces vs Banach spaces possessing a copy of $c_0$Jun 06 2019Suppose that $X$ is a Banach space. We will show that $X$ does not contain a copy of $c_0$ if and only if for each series which is not unconditionally convergent in $X$ respective sets coding all bounded subseries and rearrangements are meager. We use ... More

The forward and backward shift on the Lipschitz space of a treeJun 06 2019We initiate the study of the forward and backward shifts on the Lipschitz space of a tree, $\mathcal L$, and on the little Lipshitz space of a tree, ${\mathcal L}_0$. We determine that the forward shift is bounded both on $\mathcal L$ and on ${\mathcal ... More

Holomorphic functions with large cluster setsJun 05 2019We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed unit ball of ... More

Reflexivity and non-weakly null maximizing sequencesJun 05 2019We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize ... More

Worst-case optimal approximation with increasingly flat Gaussian kernelsJun 05 2019We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces (RKHSs) induced by increasingly flat Gaussian kernels. This provides a new perspective and some generalisations to the problem of interpolation ... More

Estimates for matrix coefficients of representationsJun 05 2019Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis and Mautner, and by Kunze and Stein. Two types of estimates have been established: ... More

On the embeddability of the family of countably branching trees into quasi-reflexive Banach spacesJun 05 2019In this note we extend to the quasi-reflexive setting the result of F. Baudier, N. Kalton and G. Lancien concerning the non-embeddability of the family of countably branching trees into reflexive Banach spaces whose Szlenk index and Szlenk index from ... More

Some remarks on $L^1$ embeddings in the subelliptic settingJun 05 2019In this paper we establish an optimal Lorentz estimate for the Riesz potential in the $L^1$ regime in the setting of a stratified group $G$: Let $Q\geq 2$ be the homogeneous dimension of $G$ and $\mathcal{I}_\alpha$ denote the Riesz potential of order ... More

Hölder continuity of quasiminimizers and $ω$-minimizers of functionals with generalized Orlicz growthJun 05 2019We show local H\"older continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, we cover more general minimizing functionals and need fewer assumptions. We prove Harnack's inequality and ... More

A residue theorem for polar analytic functions and Mellin analogues of Boas' differentiation formula and Valiron's sampling formulaJun 05 2019In this paper, we continue the study of the polar analytic functions, a notion introduced in \cite{BBMS1} and successfully applied in Mellin analysis. Here we obtain another version of the Cauchy integral formula and a residue theorem for polar Mellin ... More

Projective limits techniques for the infinite dimensional moment problemJun 04 2019We deal with the following general version of the classical moment problem: when can a linear functional on a unital commutative real algebra $A$ be represented as an integral w.r.t. a Radon measure on the character space $X(A)$ of $A$ equipped with the ... More

A Note on Estimates for Elliptic Systems with $L^1$ DataJun 04 2019In this paper we give necessary and sufficient conditions on the compatibility of a $k$th order homogeneous linear elliptic differential operator $\mathbb{A}$ and differential constraint $\mathcal{C}$ for solutions of \begin{align*} \mathbb{A} u=f\quad\text{subject ... More

Weighted and multivariate Johnson--Schechtman inequalities with application to interpolation theoryJun 04 2019We prove a weighted version of a classical inequality of Johnson and Schechtman from which we derive a decomposition theorem for $p$-th moments ($0<p\leq 1$) of nonnegative generalized $U$-statistics with constant not dependent on $p$. In particular, ... More

Hoeffding decomposition in $H^1$ spacesJun 04 2019The well known result of Bourgain and Kwapie\'n states that the projection $P_{\leq m}$ onto the subspace of the Hilbert space $L^2\left(\Omega^\infty\right)$ spanned by functions dependent on at most $m$ variables is bounded in $L^p$ with norm $\leq ... More

Toeplitz operators and pseudo-extensionsJun 04 2019There are three main results in this paper. First, we find an easily computable and simple condition which is necessary and sufficient for a commuting tuple of contractions to possess a non-zero Toeplitz operator. This condition is just that the adjoint ... More

A sharp stability criterion for single well Duffing and Duffing-like equationsJun 04 2019We refine some previous sufficient conditions for exponential stability of the linear ODE $$ u''+ cu' + (b+a(t))u = 0$$ where $b, c>0$ and $a$ is a bounded nonnegative time dependent coefficient. This allows to improve some results on uniqueness and asymptotic ... More

Uncertainty Principles for the Continuous Shearlet Transforms in Arbitrary Space DimensionsJun 04 2019The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of the Pitt's inequality for the continuous shearlet transforms, then we formulate ... More

An entire function connected with the approximation of the golden ratioJun 03 2019In 1987, R. B. Paris uses the analytic function \[\label{main} g(w)=\lim_{n\to\infty}(2\varphi)^n\biggl(\underbrace{\sqrt{1+\sqrt{1+...\sqrt{1+w}}}}_n-\varphi\biggr),\ \ \ \varphi=\frac{1+\sqrt{5}}2, \] to estimate the convergence of nested squares to ... More

An entire function connected with the approximation of the golden ratioJun 03 2019Jun 08 2019In 1987, R. B. Paris uses the analytic function \[\label{main} g(w)=\lim_{n\to\infty}(2\varphi)^n\biggl(\underbrace{\sqrt{1+\sqrt{1+...\sqrt{1+w}}}}_n-\varphi\biggr),\ \ \ \varphi=\frac{1+\sqrt{5}}2, \] to estimate the convergence of nested squares to ... More

An entire function connected with the approximation of the golden ratioJun 03 2019Jun 05 2019In 1987, R. B. Paris uses the analytic function \[\label{main} g(w)=\lim_{n\to\infty}(2\varphi)^n\biggl(\underbrace{\sqrt{1+\sqrt{1+...\sqrt{1+w}}}}_n-\varphi\biggr),\ \ \ \varphi=\frac{1+\sqrt{5}}2, \] to estimate the convergence of nested squares to ... More

Complex interpolation of families of Orlicz sequence spacesJun 03 2019We show that under general conditions complex interpolation of a family of Orlicz sequence spaces gives rise to an Orlicz sequence space, and compute the centralizer induced by the differential process, generalizing results for complex interpolation of ... More

New solution of a problem of Kolmogorov on width asymptotics in holomorphic function spacesJun 03 2019Given a domain $D$ in $\mathbb{C}^n$ and $K$ a compact subset of $D$, the set $\mathcal{A}_K^D$ of all restrictions of functions holomorphic on $D$ the modulus of which is bounded by $1$ is a compact subset of the Banach space $C(K)$ of continuous functions ... More

Localized John--Nirenberg--Campanato SpacesJun 03 2019Let $p\in(1,\infty)$, $q\in[1,\infty)$, $s\in{\mathbb Z}_{+}$, $\alpha\in[0,\infty)$ and $\mathcal{X}$ be $\mathbb R^n$ or a cube $Q_0\subsetneqq\mathbb R^n$. In this article, the authors first introduce the localized John--Nirenberg--Campanato space ... More

Von Neumann Type of Trace Inequalities for Schatten-Class OperatorsJun 03 2019We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some recent results on ... More

Resistance matrices of directed graphsJun 03 2019Let $G$ be a strongly connected and balanced directed graph. The Laplacian matrix of $G$ is then the non-symmetric matrix $L:=D-A$, where $A$ is the adjacency matrix of $G$ and $D$ is the diagonal matrix such that the row sums and the column sums of $L$ ... More

Resistance matrices of directed graphsJun 03 2019Jun 12 2019Let $G$ be a strongly connected and balanced directed graph. The Laplacian matrix of $G$ is then the matrix (not necessarily symmetric) $L:=D-A$, where $A$ is the adjacency matrix of $G$ and $D$ is the diagonal matrix such that the row sums and the column ... More

Matrix methods for wave equationsJun 02 2019In analogy to a characterisation of operator matrices generating $C_0$-semigroups due to R. Nagel (\cite{[Na89]}), we give conditions on its entries in order that a $2\times 2$ operator matrix generates a cosine operator function. We apply this to systems ... More

Laplacians with point interactions -- expected and unexpected spectral propertiesJun 02 2019We study the one-dimensional Laplace operator with point interactions on the real line identified with two copies of the half-line $[0,\infty)$. All possible boundary conditions that define generators of $C_0$-semigroups on $L^2\big([0,\infty)\big)\oplus ... More

Structural aspects of truncated archimedean vector lattices: simple elements, good sequencesJun 02 2019The truncation operation facilitates the articulation and analysis of several aspects of the structure of archimedean vector lattices; we investigate two such aspects in this article. We refer to archimedean vector lattices equipped with a truncation ... More

Monotone Relations in Hadamard SpacesJun 02 2019In this paper, the notion of $\mathcal{W}$-property for subsets of $X\times X^\loze$ is introduced and investigated, where $X$ is an Hadamard space and $X^\loze$ is its linear dual space. It is shown that an Hadamard space $X$ is flat if and only if $X\times ... More

On slow decay of Peetre's K-functionalJun 02 2019We characterize when Peetre's K-functional decays to zero slowly and we use this characterization to demonstrate certain strict inclusions between real interpolation spaces.

On $k$ point density problem for band-diagonal $M$-basesJun 01 2019In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong tridiagonal $M$-basis that was not rank one dense. Later Katavolos, Lambrou and Papadakis studied $k$ point density property of this example. ... More

Kernel Instrumental Variable RegressionJun 01 2019Instrumental variable regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available ... More

Convex Quadratic Equations and FunctionsJun 01 2019Three interconnected main results (1)-(3) are presented in closed forms. (1) Regarding the convex quadratic equation (CQE), an analytical equivalent solvability condition and parameterization of all solutions are completely formulated, in a unified framework. ... More

Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron MicroscopyMay 31 2019We develop in this paper a novel intrinsic classification algorithm -- multi-frequency class averaging (MFCA) -- for clustering noisy projection images obtained from three-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing ... More

Vertical versus horizontal Sobolev spacesMay 31 2019Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi ... More

Unbounded Order Convergence and Universal CompletionsMay 31 2019We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.

On some local Bishop-Phelps-Bollobás propertiesMay 31 2019We continue a line of study about some local versions of Bishop-Phelps-Bollob\'as type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call L$_{p, o}$ and L$_{o, p}$, and we explore ... More

The general linear equation on open connected setsMay 31 2019Fix non-zero reals $\alpha_1,\ldots,\alpha_n$ with $n\ge 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\sum_{i\le n}\alpha_iK\subseteq K$ (which holds, in particular, if $K$ is an open convex cone and $\alpha_1,\ldots,\alpha_n>0$). ... More

Analytic P-ideals and Banach spacesMay 31 2019We study the interplay between Banach space theory and theory of analytic P-ideals. Applying the observation that, up to isomorphism, all Banach spaces with unconditional bases can be constructed in a way very similar to the construction of analytic P-ideals ... More

Higher order weighted Sobolev spaces on the real line for strongly degenerate weights. Application to variational problems in elasticity of beamsMay 31 2019For one-dimensional interval and integrable weight function $w$ we define via completion a weighted Sobolev space $H^{m,p}_{\mu_w}$ of arbitrary integer order $m$. The weights in consideration may suffer strong degeneration so that, in general, functions ... More

Toeplitz operators on the domain $\{Z\in M_{2\times2}(\mathbb{C}) \mid Z Z^* < I\}$ with $\mathrm{U}(2)\times\mathbb{T}^2$-invariant symbolsMay 30 2019Let $D$ be the irreducible bounded symmetric domain of $2\times2$ complex matrices that satisfy $ZZ^* < I_2$. The biholomorphism group of $D$ is realized by $\mathrm{U}(2,2)$ with isotropy at the origin given by $\mathrm{U}(2)\times\mathrm{U}(2)$. Denote ... More

Generality of Lieb's Concavity TheoremMay 30 2019We show that Lieb's concavity theorem holds more generally for any unitarily invariant matrix function $\phi:\mathbf{H}^n_+\rightarrow \mathbb{R}$ that is monotone and concave. Concretely, we prove the joint concavity of the function $(A,B) \mapsto\phi\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big] ... More

Local theory of free noncommutative functions: germs, meromorphic functions and Hermite interpolationMay 30 2019Free analysis is a quantization of the usual function theory much like operator space theory is a quantization of classical functional analysis. Basic objects of free analysis are noncommutative functions. These are maps on tuples of matrices of all sizes ... More

Some Remarks on Schauder Bases in Lipschitz Free SpacesMay 30 2019We show that the basis constant of every retractional Schauder basis on the Free space of a graph circle increases with the radius. As a consequence, there exists a uniformly discrete subset $M\subset\mathbb{R}^2$ such that $\mathcal F(M)$ does not have ... More

Bishop-Phelps-Bollobás property for positive operators between classical Banach spacesMay 30 2019We prove that the class of positive operators from $L_\infty (\mu)$ to $L_1 (\nu)$ has the Bishop-Phelps-Bollob\'as property for any positive measures $\mu$ and $\nu$. The same result also holds for the pair $(c_0, \ell_1)$. We also provide an example ... More

On the Operator Jensen Inequality for Convex FunctionsMay 30 2019This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed ... More

On the Operator Jensen Inequality for Convex FunctionsMay 30 2019Jun 07 2019This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed ... More

Toeplitz Operators and Skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domainsMay 29 2019In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted Bergman kernel ... More

Riesz Decompositions for Schrödinger Operators on GraphsMay 29 2019We study superharmonic functions for Schr\"odinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into ... More

A $ξ$-weak Grothendieck compactness principleMay 29 2019For $0\leqslant \xi\leqslant \omega_1$, we define the notion of $\xi$-weakly precompact and $\xi$-weakly compact sets in Banach spaces and prove that a set is $\xi$-weakly precompact if and only if its weak closure is $\xi$-weakly compact. We prove a ... More

Passive discrete-time systems with a Pontryagin state spaceMay 29 2019Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides with the negative index of the ... More

Quaternionic Regularity via Analytic Functional CalculusMay 29 2019Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic approach. ... More

On the numerical index with respect to an operatorMay 29 2019Given Banach spaces $X$ and $Y$, and a norm-one operator $G\in \mathcal{L}(X,Y)$, the numerical index with respect to $G$, $n_G(X,Y)$, is the greatest constant $k\geq 0$ such that $$\max_{|w|=1}\|G+wT\|\geq 1 + k \|T\|$$ for all $T\in \mathcal{L}(X,Y)$. ... More

Berger-Coburn theorem, localized operators, and the Toeplitz algebraMay 29 2019We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of $p$-Fock spaces $(1\leq p \leq \infty)$. We present an overview of recent results by various authors on the compactness ... More

Fourier analysis associated to a vector measure on a compact groupMay 29 2019In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also introduce and ... More

Inverse approximation and GBS of bivariate Kantorovich type sampling seriesMay 28 2019In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for the space of all continuous functions with upto second order partial derivatives are continuous and bounded on $R^2.$ Further, we prove the rate of approximation ... More